integration - Evaluating $ \int_ {1/2}^ {\infty} \frac {\Gamma (u ...
5 days ago · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, …
algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b ...
Feb 21, 2025 · Well, the image equation is a different equation? One has $\frac1 {2024}$ on the right, and the other has $2024$ on the right?
calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
I am trying to evaluate the integral $$\int \frac {1} {1+x^4} \mathrm dx.$$ The integrand $\frac {1} {1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the integral if I ...
Evaluating $\\prod_{n=1}^{\\infty}\\left(1+\\frac{1}{2^n}\\right)$
Sep 13, 2016 · Compute:$$\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$$ I and my friend came across this product. Is the product till infinity equal to $1$? If no, what is the answer?
calculus - Evaluating $\int {\frac {x^ {14}+x^ {11}+x^5}
Jul 2, 2025 · The following question is taken from JEE practice set. Evaluate $\displaystyle\int {\frac {x^ {14}+x^ {11}+x^5} {\left (x^6+x^3+1\right)^3}} \, \mathrm dx$. My ...
Evaluating $\\int_0^1 (1-x^2)^n dx$ - Mathematics Stack Exchange
Mar 15, 2021 · Evaluating $\int_0^1 (1-x^2)^n dx$ [duplicate] Ask Question Asked 4 years, 9 months ago Modified 4 years, 9 months ago
Evaluating $\\int_0^{\\infty}\\frac{\\ln(x^2+1)}{x^2+1}dx$
How would I go about evaluating this integral? $$\int_0^ {\infty}\frac {\ln (x^2+1)} {x^2+1}dx.$$ What I've tried so far: I tried a semicircular integral in the positive imaginary part of the …
integration - Evaluating $\sum_ {m=0}^\infty \sum_ {n=0}^\infty …
Nov 11, 2025 · I am evaluating the following integral: $$\\int_0^{1} \\left(\\tanh^{-1}(x) + \\tan^{-1}(x)\\right)^2 \\; dx$$ After using the Taylor series of the two functions, we ...
calculus - Evaluating $\int_ {0}^ {1}\frac {x-1} { (x+1)\ln x} dx ...
Jul 3, 2020 · Evaluate the following integral $$\\displaystyle I=\\int_{0}^{1}\\frac{x-1}{(x+1)(\\ln x)} \\mathrm{d}x $$ My work: I tried it by letting $\\displaystyle I(a)=\\int ...
complex numbers - Evaluating $\cos (i)$ - Mathematics Stack …
Nov 27, 2020 · Others answered about how cos(i) c o s (i) can be calculated using Euler's formula. But I will elaborate from a different perspective. We know that cosine function can be …